Noble metal nanoparticles exhibit sharp spectral extinction peaks at visible and near-infrared frequencies due to the resonant excitation of their free electrons, termed localized surface plasmon resonance (LSPR). Since the resonant frequency is dependent on the refractive index of the nanoparticle surroundings, LSPR can be the basis for sensing molecular interactions near the nanoparticle surface. However, previous studies have not yet determined whether the LSPR mechanism can reach the ultimate sensing limit: the detection of individual molecules. Here we demonstrate single molecule LSPR detection by monitoring antibody-antigen unbinding events through the scattering spectra of individual gold bipyramids. Both experiments and finite element simulations indicate that the unbinding of single antigen molecules results in small, discrete < 0.5 nm blue-shifts of the plasmon resonance. The unbinding rate is consistent with antibody-antigen binding kinetics determined from previous ensemble experiments. According to these results, the effective refractive index of a single protein is approximately 1.54. LSPR sensing could therefore be a powerful addition to the current toolbox of single molecule detection methods since it probes interactions on long timescales and under relatively natural conditions.